If it's the same resolution it will perform the same. It's the same number of pixels in both monitors, just the pixels are spaced farther apart to fill a larger screen. Your setup is plenty of power to do some gaming and watch movies at that res (1600x1200? never seen that res but is a bit below 1920x1200)

Best to get a 1080p (1920x1080) if your goal is to watch movies. For movies and desktop apps the 560TI is overkill. For gaming though it will put more strain on it than your current resolution so you may have to lower some details on more demanding titles, but overall a 560Ti is a good card for 1080p